Answers to translating algebraic phrases worksheet.

Let’s go through each phrase one by one and turn it into an algebraic expression. We’ll use letters (like b, p, h, etc.) to stand for unknown numbers — that’s what variables are!

---

1. a number b divided by thirty-six
→ “Divided by” means fraction or division. So:
b ÷ 36 → written as b/36

2. sixty-six subtracted from a number p
→ “Subtracted from” means you start with p and take away 66.
So: p - 66

3. the quotient of twenty-nine and a number h
→ “Quotient” = result of division. So 29 divided by h.
29/h

4. a number n plus forty-nine
→ Just add 49 to n.
n + 49

5. three divided by a number g
→ 3 ÷ g → 3/g

6. the total of twenty-four and a number x
→ “Total” means addition.
24 + x

7. the difference between eighteen and a number m
→ “Difference” usually means subtraction. Since it says “between 18 and m”, we do 18 - m.
18 - m

8. a number k added to twenty-eight
→ Add k to 28 → 28 + k

9. ninety-eight more than a number d
→ “More than” means add 98 to d → d + 98

10. a number j multiplied by fifty-six
→ Multiply j by 56 → 56j (we write the number first)

11. a number y increased by eighty-six
→ “Increased by” = add → y + 86

12. twenty-nine to the wᵗʰ power
→ That’s exponentiation → 29^w

13. a number q decreased by eighty-five
→ “Decreased by” = subtract → q - 85

14. the difference between a number f and two
→ Again, difference = subtraction → f - 2

15. the quotient of a number t and thirty-seven
→ Quotient = division → t / 37

16. a number s minus eighty-two
→ Straightforward → s - 82

17. the product of a number z and eighty-four
→ Product = multiplication → z × 84 or 84z

18. a number v to the power of sixty-five
→ Exponent → v^65

19. the sum of forty-five and a number r
→ Sum = addition → 45 + r

20. the product of fifty-two and a number c
→ Product = multiplication → 52c

---

All expressions match standard algebra rules. Let me double-check a few tricky ones:

- #2: “sixty-six subtracted from p” → yes, p - 66 (not 66 - p)
- #7: “difference between 18 and m” → typically 18 - m unless specified otherwise
- #17 & #20: product → order doesn’t matter in multiplication, but convention is number first → 84z, 52c

Everything checks out.

Final Answer:
1. b/36
2. p - 66
3. 29/h
4. n + 49
5. 3/g
6. 24 + x
7. 18 - m
8. 28 + k
9. d + 98
10. 56j
11. y + 86
12. 29^w
13. q - 85
14. f - 2
15. t/37
16. s - 82
17. 84z
18. v^65
19. 45 + r
20. 52c